To find out how much the school made from potato sales, we can set up the problem with the total earnings and the earnings from the other vegetables.
We know the total earnings from the farmers' market was $256. The earnings from the other vegetables are as follows:
- Earnings from squash: $63
- Earnings from Brussels sprouts: $36
- Earnings from persimmons: $45
First, we will add the earnings from the squash, Brussels sprouts, and persimmons:
\[ 63 + 36 + 45 \]
Calculating the sum step-by-step:
- \( 63 + 36 = 99 \)
- \( 99 + 45 = 144 \)
So, the total earnings from squash, Brussels sprouts, and persimmons is \( 144 \).
Now, we will subtract this total from the overall earnings to find the earnings from potato sales:
\[ 256 - 144 = 112 \]
Thus, the school made \( \boxed{112} \) dollars from potato sales.